In A B C, C=12 13 and B C=24, then A C= ? - Vidyadip

Question

In $\triangle A B C, \cos C=\frac{12}{13}$ and $B C=24$, then $A C=$ ?

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Answer

$\cos C=\frac{12}{13}$
.....(i) [Given]
In $\triangle ABC$,
Let $\angle A B C=90^{\circ}$
$\therefore \cos C =\frac{ BC }{ AC } \quad \ldots .$. (ii) [By definition]
$\therefore \frac{ BC }{ AC }=\frac{12}{13} \ldots \ldots[$ From (i) and (ii) $]$
$\therefore \frac{24}{ AC }=\frac{12}{13}$
$\therefore \frac{24 \times 13}{12}= AC$
$\therefore \frac{312}{12}= AC$
$\therefore AC =26$ units

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